Area of quadrilateral with 2 parallel sides

What we're going to try to do in this video is find the area of this figure. We can see it's a quadrilateral; it has one, two, three, four sides. We know that this side and this side, that they're parallel to each other. You can see that they both form right angles with this dotted line. So pause this video and see if you can find the area.

All right, now if you had a little bit of trouble with that, I'll give you a hint. What if we were to take this quadrilateral and divide it into two triangles? So let me do this in a color that you are likely to see. If I were to draw a line like this, it now divides the quadrilateral into two triangles.

If I were to take this triangle right over here, I could take it out and reorient it, so it looks something, it looks something like this, where the base has length eight and then the height right over here, the height, this has length five. So that would be that triangle.

Then this triangle over here, if you were to take it out and reorient it a little bit, it could look like this, where the base is four and the triangle looks something like, looks something like this. So the base is four, and then the height is going to be five.

So this height right over here, this height, we know this is a right angle. So from here to here, which is the same thing as from here to right over here, we know that this is five. So that's my fairly big hint to you.

If you know how to find the area of a triangle, the area of a triangle we know is one half base times height. So the area of this one right over here is going to be one half times eight times five, and the area of this one over here is going to be one-half times the base, which is four, times the height, which is five.

We could evaluate each of these or we could just add them together. The area of the entire thing is going to be one-half times this base right over here, which is 8, times the height which is 5, plus plus one half times this side. You could do that as the other base times 4, times that same height times 5.

And obviously, you could just evaluate this or we could see some interesting things about it. We could express this as well. If we were to factor out a one-half and the five, this could be rewritten as one-half times eight plus four, eight plus four, and then all of that, all of that times five right over here.

So another way you could think about it is the average of the length of these two bases. You could view this as base 1 and base 2; you multiply that times the height and you have the area of this quadrilateral.

Well, what's that going to be? Eight plus four is twelve. One half times twelve, this is all going to be six. Six times five is going to be equal to thirty square units.

You could have figured it out here too: one half times eight is four, times five is twenty, and then this would have been one half times four is two, times five is ten. Twenty plus ten is thirty square units once again.